Universal frequency generation and scaling

ABSTRACT

Generation of electromagnetic or other waves of any frequency, coherence, modulation, power, etc. and for scaling such waves in frequency by any factor. Generation is achieved by incorporating an available source of desired coherence, modulation and power properties at some band of frequencies and scaling to the desired frequencies. For scaling, a continuously varied frequency selection mechanism, which results in source-distance dependent frequency scaling as described in copending applications titled “Passive distance measurement using spectral phase gradients” and “Distance-dependent spectra with uniform sampling spectrometry”, is combined with a means of determination, or prior knowledge, of the source distance. This distance, from the source to the frequency scaling mechanism, may be shortened with a refractive or dispersive medium, or varied for fine tuning of the frequency scale factor, and this variation may be effected via electrooptic or magnetooptic properties of the medium.

BACKGROUND OF THE INVENTION

1. Technical Field

This invention pertains to the generation of electromagnetic or otherwaves of desired frequency bands or the conversion of any such waves tothe desired bands. More particularly, it concerns generation of suchwaves, with desired coherence and modulation and at desired powerlevels, and conversion to or from radio frequency (RF), terahertz (THz),infrared (IR), visible, ultraviolet (UV), X-rays or even gamma ray bandswithout the current limitations due to molecular, atomic or subatomicproperties of matter.

2. Brief Description of the Prior Art

Hitherto, there has been no general mechanism for generatingelectromagnetic waves at arbitrarily chosen frequency, coherence,modulation and power level, nor to transform existing waves to achievesuch values. Technology becomes increasingly limited at THz and higherfrequencies at which the wavelengths become comparable to those of themolecular, atomic and subatomic resonances—although the latter have beenused in numerous ways to generate or modify electromagnetic waves, allsuch ways are limited to what material properties allow for suchpurposes.

For example, most of the known electromagnetic spectrum is in theorygenerated by incandescence, but the emitted power at visible or higherfrequencies is generally small. Fluorescent lamps are more efficient,but still much too noisy, weak and bulky for high bandwidthcommunication purposes. Semiconductor light-emitting diodes and laserscover much of IR and visible spectrum already, and are compact, ruggedand efficient, but their spectra are generally confined to specificoperating bands defined by the properties of the lasing media. Theemerging method of supercontinuum generation promises better coverage,but again depends on nonlinear material properties, and is inefficientand inherently broadband, which may not be suitable for applicationsrequiring specific frequencies. These constraints are generally moresevere at THz frequencies, for which there are as yet few mechanismsknown for generation in the first place. In addition, signal processingtechnology well established for audio and RF are difficult to apply atany of these higher frequencies.

As a result, the electromagnetic spectrum has four major divisions todayin terms of current technology: RF, where we can manipulate individualwaveforms and obtain coherent imaging like synthetic aperture radar(SAR); IR and visible through UV, where we get good focusing, butimaging is generally incoherent, and low noise sources (lasers) existonly for specific frequencies and bands and have low overallefficiencies; X rays and beyond where all sources are generally noisyand there is little in the way of optics; and THz, for which bothsources and control of any kind are still largely experimental.

A broad method or mechanism overcoming these constraints of wavegeneration, or enabling translation of current technological abilitiesin each of these divisions to the others, is thus desirable. Thedifficulty, as mentioned, is that these frequencies closely correspondto molecular, atomic and subatomic resonances or bond energies, whichhave prevented the generation or manipulation of these waves except aspermitted by specific molecular, atomic or subatomic structures, theirenergy levels, permitted photon transitions between these levels, and onrelated nonlinear properties of the media.

SUMMARY OF THE INVENTION

Accordingly, a primary object of the present invention is providing ageneral means for generating waves of any frequency at any combinationof modulation, coherence, polarization and power characteristics, andfor scaling such waves in frequency by any factor. A further object isto make such means available for terahertz (THz) and higher frequencies,possibly extending to infrared (IR), visible, ultraviolet (UV), X-ray oreven gamma ray frequencies.

A related object is to overcome the existing limitations in thegeneration and frequency scaling due to current dependence on molecular,atomic and subatomic energy levels and transitions, or on nonlinearproperties of materials. A further object is to enable accurategeneration or scaling of wave frequencies.

In the present invention, these and other objects which will becomeapparent are achieved by innovative exploitation of novel mechanisms forscaling frequencies in proportion to distances of wave sources that aredescribed in a first copending application, titled “Passive distancemeasurement using spectral phase gradients”, filed 2 Jul. 2004, No.10/884,353, and in a second copending application, titled“Distance-dependent spectra with uniform sampling spectrometry”, filed13 Feb. 2006 with priority of 13 Jul. 2005, No. 60/698,459, both beingincorporated herein by reference. As these mechanisms depend on sourcedistances, they are more directly suited for determining sourcedistances (ranging), by comparison with the unscaled spectra, and forextracting signals from specific sources by filtering using thedistance-scaled frequencies, as described in a third copendingapplication, titled “Distance division multiplexing”, filed 1 Mar. 2005with a priority of 24 Aug. 2004, No. 11/069,152. In the presentinvention, these mechanisms are innovatively reused for scaling thespectrum of a local wave source already having desired coherence,modulation, power level, etc. to within the frequency scale factor.

More particularly, a technique for achieving very largedistance-frequency scale factors α by means of a much smaller factor α′repetitively over a small sweep interval Δt<<1 s, such that α′=c⁻¹(αc)^(Δt/1 s), also described in the first copending application, isproposed in the present invention for realizing the desired targetfrequencies from the local source, despite its proximity as opposed tothe astronomical and terrestrial communication distances previouslyenvisaged. Additionally, the distance dependence of the frequencyscaling is envisaged as a means for optional linear control of thenormalized shift z≡δω/ω, as z otherwise depends on a normalized rate ofchange α of a physical property, and therefore has an exponentialsensitivity with respect to that property.

The referenced prior mechanisms involve an instantaneous frequencyselection {circumflex over (k)} and implement a continuous normalizedrate of change β given by

$\begin{matrix}{{\beta = {\frac{1}{\hat{k}}\frac{\mathbb{d}\hat{k}}{\mathbb{d}t}}},} & (1)\end{matrix}$to yield a frequency scale factorz=αr≡βr/c,  (2)where r is the source distance. As explained in the first copendingapplication, frequency scaling occurs, with each received wave vector k,as a shift

$\begin{matrix}{{{\delta\;\omega} = {{\frac{\partial\phi}{\partial k}\frac{\mathbb{d}\hat{k}}{\mathbb{d}t}} \equiv {\hat{\omega}\alpha\; r} \equiv {\hat{\omega}\beta\;{r/c}}}},} & (3)\end{matrix}$leading to equation (2) (z≡δω/{circumflex over (ω)}), because of thespectral gradient of phase ∂φ/∂k necessarily present in all propagatingwaves. The right side of equation (3) follows from the propagation phasecontribution kr≡ωr/c at each frequency ω≡kc, representing the commonpath delay r/c from the source, as

$\begin{matrix}{\left. {\frac{\partial\phi}{\partial k} \equiv \frac{\partial\left( {{kr} - {\omega\; t}} \right)}{\partial k}} \right|_{r,k,\omega} = {r.}} & (4)\end{matrix}$[Equation (2) then follows upon multiplying and dividing the middleexpression in equation (3) by {circumflex over (k)}.]

What happens is that to any subsequent detector, the instantaneous phaseof the waveform arriving at the detector must appear to change notmerely at the rate ∂φ/∂t=−ω given by the instantaneously selectedfrequency ω≡{circumflex over (k)}c, but with an additional contribution(∂φ/∂k)(d{circumflex over (k)}/dt) because the Fourier components(sinusoids) directed to the detector are also continuously switched withtheir phases intact, i.e. with the phases at which they arrived at thefrequency selection mechanism. The only way to avoid this contributionwould be to erase the differences in the phase offsets kr≡ωr/c in thearriving sinusoids, since these offsets have to be proportional tofrequency (ω), and thus different, in order to represent the same sourcepath delay (r/c). However, these phase offset differences are notautomatically erased by any of the fundamental frequency selectionmechanisms, including diffractive, refractive, resonant and evendigital, as considered in first and second copending applications. Thisswitching contribution, which must add the frequency shift δω was givenby equation (3) to each instantaneously selected frequency ω, was thusan oversight in all of prior physics, and is therefore novel not only inthe arts of ranging and signal processing, as considered in thecopending applications, but also in wave generation and frequencyscaling.

In the present invention, for the purpose of generating electromagneticor other waves with the desired coherence, modulation, power orpolarization characteristics, a source already possessing theseproperties to within a frequency scale factor, is combined with acontinuously variable frequency selection mechanism as described in thefirst or second copending applications.

In practice, this means a relatively short distance r, of 1 m or less,between the included source and the scaling mechanism. A normalizedshift of z−10 at r=0.1 m, to implement a device of close to this length,would require α=100 m⁻¹ or β=3×10¹⁰ s⁻¹. With repetitive sweeping withsweep intervals of Δt=100 μs, representing a sweep frequency of 10 kHz,this enormous can be achieved with a sweep change factor of Δ≡(β×1 s)¹⁰⁻⁴ =0.0024154. This is well within the magnetostrictive dynamic range ofthe “smart material” Terfenol-D, hence a grating based on this materialmight be usable as a variable diffraction grating to achieve thefrequency scaling in accordance with the first copending application. Atoptical frequencies, shorter sweep intervals, say 10 μs, could be used,reducing the sweep change to Δ=(β×1 s)¹⁰ ⁻⁵ =0.00024127, which wouldallow use of even the weaker magnetostriction of soft iron. Othermaterial properties, such as variable refractive index due toelectrooptic or magnetooptic effects, generally possess similar dynamicranges and could be alternatively utilized as means for similarlyexploiting the spectral gradient of phase in accordance with the firstor second copending applications, particularly if the polarizationrequirements permit the use of these effects.

The present invention includes innovative if opportunistic use of thesource distance dependence as an additional optional means forcontrolling the scale factor. This is useful, as mentioned, because thescale factor has an exponential dependence on the repetitive change andtherefore becomes sensitive to small variations in the latter. Forexample, α=10 m⁻¹ or β=3×10⁹ s⁻¹, i.e. frequency doubling only at 1 m,would result from a repetitive change of 0.0021846, and α=1000 m⁻¹ orβ=3×10⁹ s⁻¹ (doubling at 1 cm), would result from a repetitive change of0.0026462 both variations being less than 10% of the required value forα=100 m⁻¹. A feedback control system would be generally required inpractice to compensate for drift, but a linear control mechanism wouldbe preferable for tuning and calibration, and is generally provided bythe distance between the local source and the frequency scalingmechanism, as will become clear from the Detailed Description.

For the purpose of scaling waves already having desired coherence,modulation, power or polarization properties at a first band offrequencies, to a desired second band of frequencies, the presentinvention requires knowledge or determination of the distance r to thesource of these waves in order to set the right value fordistance-frequency scale factor α.

The source distance r may be known a priori in some scenarios. Forexample, the present invention may be used to observe the sun's UVemissions more conveniently by scaling down to visible wavelengths.Likewise, in communication technology, it would be occasionallyconvenient to transform the signals from a known base station to afrequency band more convenient for filtering, but withoutsuperheterodyning, i.e. without involving a local oscillator.

In such cases, α may be either computed or manually set to the rightvalue using a tuning mechanism. This differs from the prior applicationsin that the frequency scaling is advocated for the object of scalingitself, rather than for determining r or for isolating the signal wavesfrom a desired source from similar waves from other sources.

When the source distance r is not known, it may be separately determinedusing any among a number of ways including the distance-dependentscaling methods of the first or second copending applications, and thedetermined value of r then applied to the computation or manual settingof α as just described. A simpler alternative might be to use a feedbackcontrol system that starts with a small |α|, say |α|≈0, and raises |α|until a frequency scaled signal adequately matching the original(unscaled) waves is detected at the desired frequencies. Broad matchingcriteria should suffice since a frequency scaling application presumesunscaled source signal with some identifiable characteristics—thedistance-dependent frequency scaling mechanisms of the first and secondcopending applications as such require nonzero linespreads, precludingpure tone carriers and pure tone amplitude modulation, which would notbe so distinguishable.

Numerous variations of the invention, both by itself and in combinationwith other technologies, are envisaged and intended within its scope.For example, in an exemplary device for generating IR, optical or UVfrequencies, a medium of high refractive index may be incorporated inthe electromagnetic path between the local source and the frequencyscaling means so as permit operation with smaller r or smaller αfor thesame normalized shift z. In the presence of a refractive medium, thepath contribution to the wave phase increases to δφ=ηkr, and the resultof spectral scanning becomes

$\begin{matrix}{\left. {{\delta\;\omega} \equiv \frac{\mathbb{d}\phi}{\mathbb{d}t}} \right|_{r} = {{\frac{\mathbb{d}\hat{k}}{\mathbb{d}t}\frac{\partial}{\partial k}\left( {\eta\;{kr}} \right)} = {\hat{\omega\;}\alpha\;\eta\;{r.}}}} & (5)\end{matrix}$Thus, with a medium of η>1, the distance r between the local source andthe scaling means could be reduced by the same factor η, allowing a morecompact realization, or α reduced by η. While the latter may haveoccasional uses, the reduction of r would be more generally usefulbecause a large effective r allows finer control over z. A practicalstrategy would be to incorporate such medium for a large portion of thephysical path, leaving a small portion of the path around the source toair or vacuum, to facilitate controlled movement of the source for thefine tuning of z. This strategy especially permits use of solid media oflarge η, whereas a fluid medium of comparable η, although allowingembedded source motion, would be relatively bulky and unwieldy. Multipleloops of transmission lines, waveguides or optical fibres may be usedinstead so as to pack a substantial physical r within a small volume.

An obvious variation on the use of a refractive medium is to incorporatea medium exhibiting negative refractive index (η<1) at the sourcefrequencies. This would achieve an effectively shorter optical pathlength, which would be useful in cases where the source needs to bephysically farther than allowed for by the frequency scaling mechanismand its operating α. Such a situation may occur, for instance, with highpower sources requiring additional space for power supply and cooling.Even the frequency scaling mechanism may have to be bulkier and need tobe cooled in such cases.

A related variation is to use a normally dispersive medium, i.e. whoserefractive index increases linearly with frequency over the local sourcespectrum, so as to skew the spectral envelope of the phase offsetsfaster than propagation in free space, thereby yielding a larger scalefactor. Equation (5) becomes

$\begin{matrix}{{{{\delta\omega} \equiv {\frac{\mathbb{d}\hat{k}}{\mathbb{d}t}\frac{\partial}{\partial k}\left( {\eta\;{kr}} \right)}} = {{\hat{\omega}{\alpha\left( {{{kr}\frac{\partial\eta}{\partial k}} + {\eta\; r}} \right)}} = {\hat{\omega}\alpha\;\eta\;{r\left( {1 + {\frac{k}{\eta}\frac{\partial\eta}{\partial k}}} \right)}}}},} & (6)\end{matrix}$revealing a clear advantage to using a dispersive medium with ∂η/∂k>0.While η, is invariably a small integer, large values of (k∂η/∂k) can beachieved for specific narrow frequency bands by suitable choice ofmaterial. Such highly dispersive bands generally occur around molecularor atomic resonances. Again, it would be obvious to those skilled in therelated arts that a medium exhibiting anomalous dispersion, i.e.∂η/∂k<0, could be analogously used instead, say to physicallyaccommodate a high power source and a bulkier frequency scalingmechanism.

In these variations, a “smart material”, whose refractive index η, orindex profile ∂η/∂k can be varied dynamically say using electrooptic ormagnetooptic properties, may be used instead, as a possibly moreconvenient, “no moving parts” means for effectively varying r for tuningz, and could be clearly combined with feedback control of α for accuratetuning over a large range of z. A more mundane alternative, which may bepreferable for precision tools where bulk is of less importance, wouldbe a servo-driven mechanical screw on which either or both of the sourceand the frequency scaling mechanism are mounted, so that r can beadjusted by hand or by a servo motor.

A general, but minor, issue with the techniques of the first and secondcopending applications is that the distance-dependent shifts areinseparable from the chirping, i.e. the continuous variation offrequency represented by d{circumflex over (k)}/dt≡β{circumflex over(k)}, which means that the output waveforms are also chirps and notsinusoidal. A related problem is that not only is the outputdiscontinuous between successive sweeps, but includes the desiredfrequency only once per sweep. If the sweep were large, the output wouldhave to be accurately sampled once per sweep, and the samples somehowcombined to produce the frequency-scaled sinusoidal waveform. Forexample, successive samples could be combined by a resonator or aresistance-reactance combination that integrates the samples to producea continuous output waveform, or by a monochromator or by a spectrumanalyzer and filter combination at optical and shorter wavelengths, forthe same purpose. Samples could be similarly combined from multiplesweeps from multiple realizations of the sweep mechanism or a singlesweep mechanism with multiple outputs, like the diffractive and DSPimplementations described in the first and second copendingapplications. Fortunately, the sweep change factor Δ also defines themaximum variation of frequency in the output, and would be kept below 1%for implementational reasons, as explained, so the additional steps ofsampling and combining generally would not be required. Simpleresonators or monochromators may thus suffice in most applications, andmay be eliminated in others. Moreover, a small Δ allows faster sweeprepetition and smoother output.

Yet another basic difficulty lies in the dependence on adjacentfrequencies in the received waves, which are successively selected andcombined by the varying {circumflex over (k)}. As remarked in the firstcopending application, a nonzero bandwidth is fundamentally guaranteedfor all real signals by the fact that a perfect sinusoid, by definition,cannot have a beginning or an end, and hence cannot transport anyinformation or energy. Additionally, the principle of Green's functionsholds that every source is equivalent to a distribution of pointsources. While the traditional use of Green's functions inFresnel-Kirchhoff diffraction theory is in terms of continuous pointsource distributions¹, the principle itself does not differentiatebetween time and space coordinates, meaning that point impulsedistributions should be considered as a more general picture inclusiveof real sources with finite lifetimes. Not only does an impulse have aninfinite continuous spectrum, but all of its spectral components startat the impulse with the same phase, crucially ensuring that the spectralphase gradients ∂φ/∂k remain consistent with the actual source impulselocation at least over a differential neighbourhood of ω≡kc. Thesenotions are assuring in the cosmological context as described in thefirst copending application, where the applicable β is very small, givenby β=H₀˜10⁻¹⁸ s⁻¹. In an application of the present invention, if thesource has bandwidth less than Δ, the frequency-scaled output would beweak. A trick included in the present invention for such a source is toprovide an artificial bandwidth by modulating it with say apseudo-random sequence, which can be subsequently subtracted from thefrequency scaled output, if desired, say by reverse modulation with thesame sequence. ¹ See, for instance, the classic text, “Principles ofOptics” by M. Born and E. Wolf, Pergamon, 1959.

Numerous other objects, features, variations and advantages of thepresent invention will be apparent when the detailed description of thepreferred embodiment is considered in conjunction with the drawings,which should be construed in an illustrative and not limiting sense.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of an exemplary device illustrating the basicstructure of the present invention for the object of scalingelectromagnetic or other waves in frequency, utilizing adistance-dependent frequency scaling mechanism.

FIG. 2 illustrates the exemplary device of FIG. 1 augmented withfeedback control of the scaling factor.

FIG. 3 illustrates the exemplary device of FIG. 1 augmented withfeedback control of the physical distance from a wave source to achievefine control over the scaling factor.

FIG. 4 illustrates the exemplary device of FIG. 1 augmented with amedium of variable refractive index to achieve fine control over thescaling factor.

FIG. 5 is a block diagram of an exemplary device illustrating the basicstructure of the present invention for the object of generatingelectromagnetic or other waves at a desired set of frequencies with somedesired combination of modulation, coherence, polarization, power andother properties, utilizing a distance-dependent frequency scalingmechanism.

FIG. 6 illustrates the exemplary device of FIG. 5 augmented withfeedback control of the scaling factor.

FIG. 7 illustrates the exemplary device of FIG. 5 augmented withfeedback control of the physical distance from an included wave sourceto achieve fine control over the scaling factor.

FIG. 8 illustrates the exemplary device of FIG. 5 augmented with amedium of variable refractive index to achieve fine control over thescaling factor.

FIG. 9 is a block diagram of an improved distance-dependent frequencyscaler for possible use in the exemplary devices of FIG. 1 and FIG. 5

FIG. 10 is a graph illustrating the typical output waveform of a basicdistance-dependent frequency scaler that would be used in the exemplarydevices of FIG. 1 and FIG. 5.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The preferred embodiment of the present invention fundamentallycomprises, for the principal object of scaling electromagnetic or otherwaves, a distance-dependent frequency scaling mechanism [100] asdescribed in the first and second copending applications, involving aninstantaneous frequency selection {circumflex over (k)} and implementinga continuous normalized rate of change of selection β as defined inequation (1), in combination with a tuning means [200] for settingα≡β/c, as shown in FIG. 1.

It differs from the copending applications in that the object is thefrequency scaling itself, rather than determination of the distance r toa wave source [500] or use of the information of the dependence of thenormalized shift z on r for filtering or isolating the wave signal [510]from that source from similar waves [520], possibly overlapping infrequency, time slot, spread-spectrum coding, etc., from other sources[530], as described in the prior applications. As illustrated in FIG. 2,feedback control may be added using a sensor [120] to measure the scaledfrequencies, a frequency reference source [130], a second sensor [122]to measure the output of the frequency reference source [130], acomparator [140] to compare the outputs of both sensors [120] and [122]and to provide a feedback signal [150], in proportion to or otherwiseindicative of the difference. The feedback signal [150] is not requiredto be proportional: it would be often sufficient to generate a positiveor negative voltage of fixed magnitude indicating whether the scaledfrequencies are too high or too low relative to the frequency reference[130] by more than a threshold magnitude. Likewise, the second sensor[122] may not be needed if the frequency reference source [130] outputsan electrical signal directly, like a crystal oscillator for operationin an RF range. The feedback signal [150] may need to be conditioned bya first signal conditioner [250] before being fed back to the tuningmeans [200] to correct the normalized shift z.

While the dependence of z on r is not immediately relevant to the objectof frequency scaling, it has an optional innovative use as a means offine control of the normalized shift z. The innovative, opportunisticuse of the r-dependence lies in feeding the output of the comparator[140] via a second conditioner [252] to change the effective sourcedistance r, either by increasing the actual physical distance betweenthe wave source [500] and the distance-dependent frequency scalingmechanism [100] using a distance adjustment means [260] or by varyingthe refractive index η of an electro-optic or magneto-optic device [600]located between the wave source [500] and the distance-dependentfrequency scaling mechanism [100]. In the latter case, since theelectro-optic or magneto-optic device [600] will only occupy a smallportion of the overall distance r, and refractive indices are ordinarilysmall, very precise control would be realized over the normalized shiftz. These three methods of control, i.e. of α, r or η, may beincorporated and used individually, or combined in various ways, in agiven instrument.

A frequency scaler as just described can be combined with a suitablewave source to obtain a generator of waves of any desired scaledfrequencies. More specifically, a tunable scaler can be used with asource possessing a fixed frequency or a limited operating range offrequencies to realize a source able to generate waves over a muchlarger range of frequencies by scaling. Modulation, polarization, powerand other properties of the combined source can be preserved providedthese properties are not substantially altered by the frequency scalingmechanism and its associated control systems if any.

FIG. 5 illustrates this inventive combination of a frequency scalingmechanism [100] as described in the prior applications, with a source[500] emitting signal waves [510] having modulation, polarization, powerand other characteristics as may be desired, but at a first band offrequencies around ω₁, so as to produce waves of similar properties at asecond, desired band of frequencies around ω₂ by scaling the signalwaves [510] using a normalized shift z=ω₂/ω₁−1. FIG. 6 shows thecorresponding feedback control of the scaling factor α. FIG. 7illustrates the corresponding distance-based control of the normalizedfrequency shift z by varying the physical distance r of the wave source[500] from the frequency scaling mechanism [100], analogous to theinventive device of FIG. 3. FIG. 8 shows the correspondingdistance-based control by varying the effective path length r of thewave source [500] from the frequency scaling mechanism [100], using anelectro-optic or magneto-optic device [600] just like in the inventivescaler of FIG. 4. Both FIG. 7 and FIG. 8 also show simultaneous controlof α, as do FIGS. 3 and 4, purely to illustrate how the three methods ofcontrol may be combined in a given receiver implementing the presentinvention.

Finally, the source bandwidth, necessary for the frequency scaling asexplained in the Summary and the referenced copending applications,could turn out to be inadequate in some cases and may be enhanced bymodulation, as shown in FIG. 9, with a known signal f(t), such as apseudo-random sequence from another source [300], using a multiplier orother modulation means [310]. The modulated waveform is then given asinput, in place of the original waves [510], to the actual frequencyscaling mechanism [110], which applies a changing instantaneousfrequency selection at the change rate of β≡αc to repetitively sweep thespectrum of the input wave signal [510], as treated in the first andsecond copending applications, to produce the desired frequency scalingas explained in the Summary. The known signal f(t)'s content may be thensubtracted from the output of the actual frequency scaling mechanism[110] by a second multiplier or other modulation-subtractor means [320],which would generally need access to f(t) for reference.

This subsequent subtraction of the modulating known signal may beunnecessary in some applications, e.g. where the need is simply forillumination around the desired scaled frequency. In such cases, theoutput of the actual frequency scaling mechanism [110] can be useddirectly and the second multiplier or other modulation-subtraction means[320] can be eliminated. (An alternative combination of the actualfrequency scaling mechanism [110] with the second multiplier or othermodulation-subtractor means [320] would be merely equivalent to amodulation of the output of the general frequency scaling mechanism[100] of FIG. 1.) This combination of a known signal source [300], afirst multiplier or other modulation means [310] and an optional secondmultiplier or other modulation-subtractor means [320] along with anactual frequency scaling mechanism [110] corresponds to, and wouldreplace, the distance-dependent frequency scaling mechanism [100] forfrequency scaling sources of insufficient bandwidth.

FIG. 9 further includes an optional post-filter [350] for extracting thedesired scaled frequency from the output of the actual frequency scalingmechanism [110] and the optional second multiplier or othermodulation-subtractor means [320], as this output waveform will beinherently a chirp and not sinusoidal, as remarked in the Summary. Morespecifically, since the actual distance-dependent frequency scalingmechanism [110] functions by sweeping the spectrum of the input wavesignal [510], its instantaneous frequency selection {circumflex over(ω)}(t) necessarily comprises a succession of chirps each correspondingto a single sweep, likely separated by blanking intervals. The outputwaveform (FIG. 10) would ideally follow {circumflex over (ω)}(t) exceptfor the frequency scale factor (1+z)≡(1+αr), with a similar successionof chirps [400] and blanking intervals [410] in between. FIG. 10represents only the ideal case of a point impulse source because withmost sources, the contributions within each chirp will not have equalamplitude, so in general, the chirps will not exhibit a uniformamplitude as shown.

However, as explained in the Summary, the total variation Δ of theinstantaneous frequency during each chirp is as such likely to be smallfor reasons having to do with the implementation of thedistance-dependent frequency scaling mechanism [100] or the actualfrequency scaling mechanism [110], and that even otherwise, it isdesirable to keep Δ small to allow fast repetition of the sweeps. So thefrequency and amplitude variations within a chirp should not generallymatter.

It would be obvious to those skilled in the related arts that it wouldbe further desirable to minimize the blanking intervals [410], andfurther that a fairly pure sinsoidal signal of the desired scaledfrequency can be readily extracted, where particularly desired, in oneof several ways of implementing the post-filter [350], including

-   -   passing the waveform through a band-pass filter, a physical        resonator or a resonant circuit tuned to the desired scaled        frequency;    -   sampling the chirps at precise sampling instants [420] when the        instantaneous frequency just matches the desired scaled        frequency and combining the resulting succession of sample        energies (or voltages or currents or electromagnetic field        strengths or acoustic displacements or pressures) to obtain the        output (sinusoidal) waveform;    -   in diffractive implementations of the actual distance-dependent        frequency scaling mechanism [110] as described in the first and        second copending applications, sampling as above at two or more        angles of diffraction and optionally combining these sample        streams to obtain a stronger output signal;    -   and combining two or more actual frequency scaling mechanisms to        sweep the input wave signal [510] in parallel, synchronously, or        at the same sweep rate but with overlapping sweeps, or at        different sweep rates altogether, to obtain a stronger output        signal.        The filtering approach would be generally simpler and yield a        stronger output signal combining the total energy of each chirp,        whereas sampling will likely diminish the output power. In        either case, an almost pure sinusoidal signal of the desired        scaled frequency would result that closely follows the variation        over time of the amplitude, phase and other properties of the        original input wave signal [510], subject only to some        distortion of these properties by the band-pass filtering or        inaccuracy in the synthesis.

Although the invention has been described above with reference to thepreferred embodiment, it will be appreciated by one of ordinary skill inthe arts of physics, electronics and communication technologies thatnumerous modifications and variations are possible in the light of theabove disclosure. For example, the inventive method could be conceivablyapplied to sound and to communication under water. All the componentfunctions other than the distance-dependent frequency scaling mechanisms([100] and [110]) are known in both acoustic and electromagnetictechnologies, and in both analogue and digital signal processing fields,and as such, can be variously implemented by those skilled in therespective arts. Thus, for instance, the comparator [140], theconditioner [250] and the tuner [200] would be generally electricaldevices connected by wires as shown in the figures, but could beimplemented by analogous mechanical devices, in submarine applicationsor on the nanoscale. They could be also replaced by equivalent opticaldevices and the wiring could be replaced by optical fibres, transmissionlines, radio channels or a suitable digital network. For thedistance-dependent frequency scaling mechanisms ([100] and [110]), thefirst and second copending applications similarly identify numerousimplementation strategies suited to various forms of input waves, in allthree basic classes of frequency selection, viz resonant, diffractiveand digital, and it would be clear to the skilled practitioner that allthree approaches could be applied to electrical signals, sound, andelectromagnetic waves including visible and higher frequencies.Similarly, the post-filter [350] may comprise a combination of a slit,to select the output chirps at a desired diffraction angle, a secondFourier spectrometer to spread the component frequencies of the chirpsand a second slit to select one of these component frequencies, as analternative to the time-domain approach of sampling. Further, thepost-filter [350] may be applied to the output of the distance-dependentfrequency scaling mechanism [100], i.e. to the equivalent actualfrequency scaling mechanism [110] without the first multiplier or othermodulation means [310] and known signal source [300].

All such modifications, generalizations and variations are intendedwithin the scope and spirit of the invention as defined in the claimsappended hereto.

1. A device for scaling electromagnetic or other waves from an externalsource at a nonzero distance r arriving at a first band of frequenciesω₁ to a second band of frequencies ω₂, the device comprising acontinuously variable frequency selection means, wherein thecontinuously variable frequency selection means is varied at anormalized rate β, in order to achieve the scaling of the frequencies ofthe electromagnetic or other waves, and the normalized rate β is set toa wave speed c times the ratio of the difference between the second andthe first bands of frequencies to the first band of frequencies dividedby the distance r between the external source and the continuouslyvariable frequency selection means, to c·(ω₂−ω₁)/(ω₁·r).
 2. The deviceof claim 1 further including a feedback control means to dynamicallycompare the output of the continuously variable frequency selectionmeans with the first band of frequencies ω₁, and to accordingly correctthe normalized rate, thereby ensuring that the second band offrequencies ω₂ results.
 3. The device of claim 1 further including amodulation means before the continuously variable frequency selectionmeans, an optional modulation-subtractor means after the continuouslyvariable frequency selection means, and a known signal, wherein themodulation means modulates the electromagnetic or other waves with theknown signal, and the optional modulation-subtractor means, if present,eliminates the known signal modulation from the electromagnetic or otherwaves.
 4. The device of claim 1 further including a post-filter meansfor refining or extracting the second band of frequencies ω₂, locatedafter the continuously variable frequency selection means.
 5. A devicefor generating electromagnetic or other waves at a first band offrequencies ω₁, the device comprising an internal source producing saidelectromagnetic or other waves at a second band of frequencies ω₂, and acontinuously variable frequency selection means located at a nonzerodistance r from the internal source, wherein the continuously variablefrequency selection means selects a continuously changing frequency inthe electromagnetic or other waves from the internal source and thefrequency selection is varied at a normalized rate β set to a wave speedc times the ratio of the difference between the second and the firstbands of frequencies to the first band of frequencies divided by thedistance r from the internal source to the continuously variablefrequency selection means, to c·(ω₂−ω₁)/(ω₁·r).
 6. The device of claim 5further including a feedback control means to dynamically compare theoutput of the continuously variable frequency selection means with thefirst band of frequencies ω₁ and to accordingly correct the normalizedrate β in order to ensure that the second band of frequencies ω₂results.
 7. The device of claim 5 further including a feedback controlmeans to dynamically compare the output of the continuously variablefrequency selection means with the first band of frequencies ω₁ and toaccordingly vary the distance r between the internal source and thecontinuously variable frequency selection means so as to ensure that thesecond band of frequencies ω₂ results.
 8. The device of claim 5 furtherincluding a possibly dispersive medium of nonunity refractive indexbetween the internal source and the continuously variable frequencyselection means to shorten or adjust the distance r between the internalsource and the continuously variable frequency selection means.
 9. Thedevice of claim 7 further including a possibly dispersive medium ofvariable refractive index between the internal source and thecontinuously variable frequency selection means, wherein effectivevariation of the distance r between the internal source and thecontinuously variable frequency selection means is achieved by varyingthe refractive index of the medium.
 10. The device of claim 5 furtherincluding a modulation means before the continuously variable frequencyselection means, an optional modulation-subtractor means after thecontinuously variable frequency selection means, and a known signal,wherein the modulation means modulates the electromagnetic or otherwaves with the known signal, and the optional modulation-subtractormeans, if present, eliminates the known signal modulation from theelectromagnetic or other waves.
 11. The device of claim 5 furtherincluding a post-filter means for refining or extracting the second bandof frequencies ω₂, located after the continuously variable frequencyselection means or after the optional modulation-subtractor means.
 12. Amethod for generating electromagnetic or other waves or scalingelectromagnetic or other waves emitted by a source, from a first band offrequencies ω₁ to a second band of frequencies ω₂, in a device includinga continuously variable frequency selection means, the method comprisingthe step of continuously varying the frequency selection at a normalizedrate β set to a wave speed c times the ratio of the difference betweenthe second and the first bands of frequencies to the first band offrequencies divided by the distance r from the source to thecontinuously variable frequency selection means, to c·(ω₂−ω₁)/(ω₁·r).13. The method of claim 12 in a device further including a feedbackcontrol means to dynamically compare the output of the continuouslyvariable frequency selection means with the first band of frequenciesω₁, the method additionally comprising the step of dynamicallycorrecting the normalized rate in order to ensure that the second bandof frequencies ω₂ results.
 14. The method of claim 12 in a devicefurther including a feedback control means to dynamically compare theoutput of the continuously variable frequency selection means with thefirst band of frequencies ω₁, the method additionally comprising thestep of dynamically varying the distance r from the source to thecontinuously variable frequency selection means, in order to ensure thatthe second band of frequencies ω₂ results.
 15. The method of claim 14 ina device additionally including a possibly dispersive medium of variablerefractive index between the source and the continuously variablefrequency selection means, wherein the step of varying the distance rbetween the source and the continuously variable frequency selectionmeans is performed in effect by varying the refractive index of themedium.
 16. The method of claim 12, wherein the device further includesa possibly dispersive medium of nonunity refractive index between thesource and the continuously variable frequency selection means.
 17. Themethod of claim 12, including the additional steps of first modulatingthe electromagnetic or other waves with a known signal before scaling ofsaid electromagnetic or other waves from the first band of frequenciesω₁ to the second band of frequencies ω₂, and optionally removing thisknown signal modulation from the electromagnetic or other waves aftersaid scaling to the second band of frequencies ω₂.
 18. The method ofclaim 12, including an additional step of post-filtering theelectromagnetic or other waves after said scaling to refine or extractthe second band of frequencies ω₂.